Abstract

The actin cytoskeleton is a biopolymer network that provides spatial coordination and mechanical strength to biological cells. Due to the asymmetric mechanical response of polymers under tension versus compression, it behaves like a mechanical network of cables. In addition, it actively contracts through the continuous action of myosin molecular motors. Here we investigate theoretical models on the cellular scale which incorporate these special properties. In the first part of this work we model cells adherent to discrete adhesion sites on planar surfaces. We compare the shape and force distribution in contracted networks of Hookean springs and cables. We find that only active cable networks can correctly predict the experimentally observed cell shape. In the second part we apply the active cable network to experimental data. We combine this model with contractile actin bundles and find that this combination leads to surprisingly good predictions for the traction force pattern of adherent cells on soft elastic substrates. Because cellular forces can lead to failure of the network, in the third part we investigate bond rupture in mechanical networks. Here, bonds stochastically rupture with rates that grow exponentially with force. We study the statistical properties of networks under constant strain and strain which linearly increases in time. The results are compared to traditional fracture mechanics which are dominated by stability thresholds.